1. Thermal 2007T.Umeda (Tsukuba)1 Constant mode in charmonium correlation functions Takashi Umeda This is based on the Phys. Rev. D75 094502 (2007) Thermal Field Theory and their applications YITP Kyoto, 5-7 September 2007 [hep-lat/0701005]

2. Thermal 2007T.Umeda (Tsukuba)2 Experiments SPS : CERN ( – 2005) Super Proton Synchrotron RHIC: BNL (2000 – ) Relativistic Heavy Ion Collider LHC : CERN (2009 - ) Large Hadron Collider from the Phenix group web-site

3. Thermal 2007T.Umeda (Tsukuba)3 First paper on the J/ψsuppression photo : Prof. Osamu Miyamura

4. Thermal 2007T.Umeda (Tsukuba)4 J/ψ suppression in Exp. Phys.Lett.B477(2000)28 NA50 Collaboration QM2006 PHENIX Collaboration “Charmonium states in QGP exist or not ?” from Lattice QCD Energy density 0.5-1.5GeV/fm 3 = 1.0Tc 10 GeV/fm 3 = 1.5Tc 30 GeV/fm 3 = 2.0Tc

5. Thermal 2007T.Umeda (Tsukuba)5 Charmonium in Lattice QCD Path integral by MC integration Lattice QCD enables us to perform nonperturbative calculations of QCD QCD action on a lattice Input parameters (lattice setup) : (1) gauge coupling  lattice spacing (a)  continuum limit (2) quark masses (3) (Imaginary) time extent  Temperature (T=1/Nta) Wilson quark, Staggered (KS) quark, Domain Wall quark, etc

6. Thermal 2007T.Umeda (Tsukuba)6 Charmonium correlation function Correlation function Pseudescalar(Ps) J PC = 0-+ η c,... Vector (V) J PC = 1-- J/ψ, ψ(2S),... Scalar (S) J PC = 0++ χ c0,... Axialvector (Av) J PC = 1++ χ c1,... Charmonium operators LQCD provides C(t) of charmonium at T>0

7. Thermal 2007T.Umeda (Tsukuba)7 Example of lattice results ?

8. Thermal 2007T.Umeda (Tsukuba)8 Charmonium spectral function Quenched QCD - T. Umeda et al., EPJC39S1, 9, (2005). - S. Datta et al., PRD69, 094507, (2004). - T. Hatsuda & M. Asakawa, PRL92, 012001, (2004). - A. Jakovac et al., PRD75, 014506 (2007). Full QCD - G. Aarts et al., hep-lat/0610065. Maximum entropy method C(t)  ρ(ω) All studies indicate survival of J/ψ state above T c (1.5T c ?)

9. Thermal 2007T.Umeda (Tsukuba)9 Sequential J/ψsuppression Particle Data Group (2006) PsV S Av E705 Collaboration, PRL70, 383, (1993). 10% 30% 60% Dissociation temperatures of J/ψ and ψ’& χ c are important for QGP phenomenology. for the total yield of J/ψ

10. Thermal 2007T.Umeda (Tsukuba)10 Discussion (*) They concluded that the results of SPFs for P-states are not so reliable. e.g. large default model dep. the drastic change just above Tc is reliable results. Studies for P-wave charmonium SPFs S. Datta et al., PRD69, 094507 (2004). A.Jakovac et al., PRD75, 014506 (2007).

11. Thermal 2007T.Umeda (Tsukuba)11 Lattice QCD results Lattice setup Quenched approximation ( no dynamical quark effect ) Anisotropic lattices lattice size : 20 3 x N t lattice spacing : 1/a s = 2.03(1) GeV, anisotropy : a s /a t = 4 Quark mass charm quark (tuned with J/ψ mass) t x,y,z

12. Thermal 2007T.Umeda (Tsukuba)12 Effective mass (local mass) Definition of effective mass In the (anti) periodic b.c. when

13. Thermal 2007T.Umeda (Tsukuba)13 Effective mass (local mass)

14. Thermal 2007T.Umeda (Tsukuba)14 At zero temperature (our lattice results) M PS = 3033(19) MeV M V = 3107(19) MeV (exp. results from PDG06) M ηc = 2980 MeV M J/ψ = 3097 MeV M χc0 = 3415 MeV M χc1 = 3511 MeV In our lattice N t ⋍ 28 at T c t = 1 – 14 is available near T c Spatially extended (smeared) op. is discussed later

15. Thermal 2007T.Umeda (Tsukuba)15 Quenched QCD at T>0 small change in S-wave states  survival of J/ψ & η c at T>T c drastic change in P-wave states  dissociation of χ c just above Tc (?) S. Datta et al., PRD69, 094507 (2004). etc...

16. Thermal 2007T.Umeda (Tsukuba)16 Constant mode Pentaquark (KN state): two pion state:  Dirichlet b.c. c.f. T.T.Takahashi et al., PRD71, 114509 (2005). exp(-m q t) x exp(-m q t) = exp(-2m q t) exp(-m q t) x exp(-m q (L t -t)) = exp(-m q L t ) m q is quark mass or single quark energy L t = temporal extent in imaginary time formalism L t = 1/Temp. gauge field : periodic b.c. quark field : anti-periodic b.c. in confined phase: m q is infinite  the effect appears only in deconfined phase

17. Thermal 2007T.Umeda (Tsukuba)17 Free quark calculations Continuum form of the correlators calculated by S. Sasaki : single quark energy with relative mom. p where

18. Thermal 2007T.Umeda (Tsukuba)18 Physical interpretation constant contribution remains in the continuum form & infinite volume The constant term is related to some transport coefficients. From Kubo-formula, for example, a derivative of the SPF in the V channel is related to the electrical conductivity σ. F. Karsch et al., PRD68, 014504 (2003). G. Aarts et al., NPB726, 93 (2005).

19. Thermal 2007T.Umeda (Tsukuba)19 Without constant mode How much does SPF change at the region from “An Introduction to Quantum Field Theory” Michael E. Peskin, Perseus books (1995)

20. Thermal 2007T.Umeda (Tsukuba)20 Midpoint subtraction An analysis to avoid the constant mode Midpoint subtracted correlator Free quarks

21. Thermal 2007T.Umeda (Tsukuba)21 Midpoint subtraction analysis usual effective masses at T>0 the drastic change in P-wave states disappears in m eff sub (t)  the change is due to the constant mode subtracted effective mass 0.1a t =800MeV

22. Thermal 2007T.Umeda (Tsukuba)22 Results with extended op. extended op. enhances overlap small constant effect in V channel no large change above T c in m eff sub (t) usual effective masssubtracted effective mass Spatially extended operators: with a smearing func. φ(x) in Coulomb gauge

23. Thermal 2007T.Umeda (Tsukuba)23 Discussion The drastic change of P-wave states is due to the const. contribution.  There are small changes in SPFs ( except for ω=0 peak ). Why several MEM studies show the dissociation of χ c states ? point operatorsextended operators

24. Thermal 2007T.Umeda (Tsukuba)24 Conclusion There is the constant mode in charmonium correlators above T c The drastic change in χ c states is due to the constant mode  the survival of χ c states above T c, at least T=1.4T c. The result may affect the scenario of J/ψ suppression. In the MEM analysis, one has to check consistency of the results at using, e.g., midpoint subtracted correlators.